Brother Jed takes heathens and reforms them into righteous individuals. There are two inputs needed in this process: heathens (who are widely available) and preaching. The production function has the following form: r_p = min{h, p}, where r_p is the number of righteous persons produced,his the number of heathens who attend Jed’s sermons, and p is the number of hours of preaching. For every person converted, Jed receives a payment of s from the grateful convert. Sad to say, heathens do not flock to Jed’s sermons of their own accord. Jed must offer heathens a payment of w to attract them to his sermons. Suppose the amount of p reaching is fixed at p̅ and that Jed is a profit-maximizing profit.

(a) If h < p̅, what is the marginal product of heathens __________. What is the value of the marginal product of an additional heathen __________.

(b) If h > p̅, what is the marginal product of heathens __________. What is the value of the marginal product of an additional heathen in this case __________.

(c) Sketch the shape of this production function in the graph below. Label the axes, and indicate the amount of the input where h = p̅.

(d) If w < s, how many heathens will be converted ________?. If w > s, how many heathens will be converted ___________?